You could use this sentence in many different situations. Mostly though it is used to express something that you thought was X but it turned out to be Y or Z instead.

Example: If you thought you were supposed to meet a friend at the movies at 8, but really it was 7, you could say to your friend, "I'm sorry. I was mistaken about the time." Or, if you approached someone on the street that you thought was your friend but it turns out that it was actually a stranger you could say, "I was mistaken."

(Sidenote: The more I look at the word "mistaken" it really sounds strange to me! I don't know why... haha)

Thank you correcting me.
And you gave me the useful comment.

I thought that sentence mean:

　　　　　　　 past present　　　　　future
－－－－－－○－－－－－－○－－－－－－
－－－－－→×－－－－－→×
　　　　 "I'm wrong..." 　　　 "I had mistaken about that."

But maybe I understood about it.
Thank you, kissncry.